Tinting and/or coloring paper by the use of colorants, such as dyes and optical brightening agents (OBAs) has been common for many years in the operation of paper making machines. The actual sheet or web color is determined by measuring the reflectance spectrum of the web sheet as it travels through the production process. For example, measurement may be performed by an online spectrophotometer that measures the reflectance spectrum of the sheet. Dye additions can be made at different stages of the paper making process to achieve a desired color shade.
The spectrophotometer is typically mounted to a scanning device for continuously measuring sheet color reflectance spectrum from a standard light source that is directed at one side of the sheet, with a backing background on the opposite side of the sheet chosen for reducing opacity effects. The measured sheet reflectance spectrum range is typically from 360 to 720 nm in wavelength, covering the range of visible light wavelengths plus a portion of the ultra-violet spectrum. By using a set of standard non-linear equations, the sheet reflectance spectrum can be used to calculate sheet color in terms of various defined coordinate systems, for example CIE L*, a*, b* values, where L* represents a lightness axis ranging from 0 for black and 100 for white, a* represents a red-green axis where a positive number is indicative of redness while a negative number is indicative of greenness, and b* represents a blue-yellow axis where a positive number is indicative of yellowness while a negative number is indicative of more blueness.
Control of the sheet color using a set of dyes requires knowledge of the response model for each dye, which is typically represented by sheet color reflectance spectrum value change given a normalized dye flow ratio change, for example, pound-per-ton of fiber stock used to make the paper. With knowledge of the sheet target value (Lt, at, bt) and measured sheet value (Lm, am, bm) and the response model for each dye, a control algorithm can be used to calculate the dye flow ratio change for minimizing sheet color error from the target value, normally represented by ΔE, as follows: ΔE=sqrt[(Lt−Lm)2+(at−am)2+(bt−bm)2].
The dye response model (i.e. reflectance spectrum value change per unit dye ratio change) is normally obtained through the use of a “bump” test. For example, under normal operating conditions with manual color control and a stable production process, the measured sheet reflectance spectrum value change is calculated before and after a dye ratio change and the normalized spectrum difference is used for the dye response model. This model has been found to be valid for paper production of similar sheet color as produced during the “bump’ test.
Color changes made during the production of paper often result in ‘off-spec’ sheet material being produced, both during and after such color changes. This ‘off-spec’ web, referred to as color broke, is typically recycled back to the early stages of production. Accordingly, one of the goals in sheet color control is to develop an accurate dye response model that quickly minimizes the error between the measured sheet color and the target color, thereby reducing the occurrence of sheets that are off-specification during and following a grade change or at start-up or as a result of disturbances that may occur during steady-state, and thereby also reducing costs.
It is also known in the prior art to model the steady state behaviour of the coloring process by determining a steady state gain from the dye flow to the measured color at different concentrations, or by spectral response models obtained by dye response tests. One example of dye response model gain adaptation is described in U.S. Pat. No. 6,052,194 (Nuyan), the contents of which are incorporated herein by reference. In either dye response model gain adaptation or spectral response modelling, the resulting model is grade-dependent. This grade dependency is especially severe in the case of dye response model gain adaptation because of the highly non-linear relationship of measured color to the measured sheet spectrum.
The dye response model, described above, can be decomposed into a normalized response shape over the spectrum range (360 to 720 nm, with unit gain), and associated with a response gain (i.e. a scalar) for gain adaptation by creating a non-linear table of actual dye flow ratio used and the associated response gain, while keeping the response shape constant. The non-linear table may be calculated using a series of bump tests during the production process using different dye ratios. When using this type of gain adaptation, a base flow must be added to the actual dye flow in order to represent an “equivalent” amount of dye in the broke stock.
The model gain and base flow relation is highly non-linear. For instance, the gain difference could be as high as several thousand folds when producing light shade color (normally low dosage of dye) and dark shade color (normally high dosage) of paper. To get an accurate relation of gain-base flow curve, many “bump” tests were needed.
There are at least two issues that have limited the use of the dye response model gain adaptation set forth above. First, it has been observed that when producing a deep shade color paper, the actual dye response gain is significantly smaller than when producing light shade color paper for the same dye using a similar dye ratio. Second, when a large amount of broke is used as furnish, there is no accurate way to estimate the corresponding base flow (added offset of a dye flow) of the dye. It has been reported that the amount of broke can be as high as 80% in extreme cases.
Furthermore, it has been discovered that the dye response shape over the spectrum can depend on the measured sheet color, especially when the sheet color shade is dark. The difference can in some circumstances be so large that the resulting control action is in the opposite direction to the predicted response based on dye flows.